Beverton-Holt Model of a Commercial Fishery: Optimal Dynamics

The problem of optimal regulation of a fishery is discussed. Of special interest is the problem of regulating an overexploited fishery by reducing effort to allow the fish population to build up to a suitable level.We first argue that the problem requires an economic analysis based on the concept of maximization of present value. From this concept we then deduce a simple, general rule, the "Fisher Rule," which we subsequently use to determine optimal exploitation. Among the principal results are the following: (a) an optimal mesh-size is determined, which, because of the discounting of future revenues, is smaller than the size corresponding to maximum sustainable yield; (b) the optimal recovery policy for an overexploited fishery is deduced; it consists of a fishing closure permitting the fish population to reach an optimal age; (c) the optimal development of an unexploited fishery is deduced; an initial development stage characterized by large landings and profits is rapidly transformed into a situation ...